Advancing Multiparametric Programming for Model Predictive Control

Model predictive control provides the optimal operation for chemical processes by explicitly accounting for the system, constraints, and costs. In an online setting, developing the implicit optimal control action under time consideration is non-trivial. Over a decade ago, it was demonstrated through multiparametric programming that the implicit control law defining the model predictive controller can be determined explicitly, once and offline. The benefit of such an approach is the (i) improved online computational time, (ii) the development of the offline map of solution \textit{a priori}, and (iii) the derivation of the optimal control laws under any state variation. In recent years there has been a significant push for the development of novel algorithms and theoretical advancements for multiparametric model predictive control. These algorithms and theoretical underpinnings have expanded the problem classes that are solvable and improved the computational efficiency. However, there is still a need to provide analysis for formulations based on different surrogate models, and to tackle large scale multiparametric model predictive control problems. In this dissertation, the research focus is (i) the inclusion of a new surrogate modeling technique from the machine learning community, (ii) developing a criterion to compare multiparametric model predictive control formulations based on different surrogate models, (iii) the development of an algorithm to solve large scale multiparametric optimization problems, and (iv) improving the online computational performance of online solvers via multiparametric programming. To this end, tools from data science, computational geometry, and the operations research community contributed greatly to the results presented in this work. This research is verified via the optimal operation of chemical engineering processes and the efficacy of the developed algorithms is demonstrated on computational studies